I’ve transcribed it. The scene is Trump is coming off the stage, likely exhausted and flustered, and a reporter is amongst a crowd of autograph seekers.

REPORTER: “Should there be a database system who tracks the Muslims that are in this country?”

TRUMP: “There should be a lot of systems, beyond databases. We should have a lot of systems. And today you can do it. But right now we have to have a border, we have to have strength, we have to have a wall. And we cannot let what’s happening to this country happen [again? inaudible].”

REPORTER: “Is that something your White House would like to implement?” [NOTICE: What is “that”? The reporter kept it vague. Why? Gee, I wonder! Journalism 101 on how to get a “gotcha” quote from a politician where your question isn’t clear and while they’re distracted.)

TRUMP: “Oh, I would certainly implement that. Absolutely.”

REPORTER: “What do you think the effect of that would be? How would that work?”

TRUMP: “It would stop people from coming in illegally. We have to stop people from coming into our country illegally.” [So, explain to me how Trump is referring to a registration of “all Muslims”, much less “all Muslims” in the U.S., when, whatever he is referring to, he says would be about stopping people “from coming in illegally”?]

REPORTER: “But more specifically how do you actually get them registered in the database….?”

TRUMP: “It’s would be just good management. What you have to do is good management procedures. And we can do that.”

REPORTER: “I mean, do you go to the mosques and sign these people up and into the system?”

TRUMP: “Different places. You sign em up at different places. But it’s all about management. Our country has no management.”

REPORTER: “Would they have to legally be in this database?”

TRUMP: “They have to be – they have to be, let me just tell you: that the key is people can come to the country but they have to come in legally. Thank you very much.”

So even when concluding, Trump is talking about illegal immigration and registrations/databases pertaining to THAT — not to “all” Muslims and certainly not all all Muslims “in the U.S.” At the very least, he and the reporter seem to be talking past each other. Trump makes it clear TWICE that he’s referring to illegal immigration and yet somehow this has turned into “Trump wants every Muslim in the U.S. to be registered in a database.”

Another point worth noting is, considering the loud atmosphere, Trump (and any reasonable person), I believe interpreted the question to be about Muslims “coming into” rather than “in” the U.S. (which also would then perfectly explain why he mentions immigration and thinks that’s what the reporter is asking about). In other words, that the question was: “Should there be a database system who tracks the Muslims that are coming into [vs “in] this country?” Especially since it makes sense to ask about Muslims “coming in” in light of the fact that THAT’s what the current controversy is about (the Syrian refugees). Consider how that changes the “controversial” nature of his answer, particularly, when, well, immigrants are ALREADY IN A DATABASE.